Pavel Strnsk
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Last updated: 11.12.2024

Program Collective Models

Calculation, visualisation and analysis of classical and quantum Hamiltonian systems and time series

The program requires .NET Framework 2.0. Therefore, in can be run natively under the operation systems Microsoft Windows Xp, Vista, 7. Under Linux, BSD, Mac OS X it is possible to use the products Mono or DotGNU (however, the complete function of the program is not guaranteed).

Version 0.9.9.2 (15th March 2012)
All platforms: ZIP archive (6.56MB)
Changes and new functions:
Version 0.9.9.1 (18th January 2010)
All platforms: ZIP archive (3.85MB)
Forced 32-bit: ZIP archive (3.85MB)
Changes and new functions:
  • A procedure that distinguishes using the SALI method between a regular and chaotic trajectory has been modified and improved.
  • The computation methods of the SALI has been extended - it is allowed now to change the precicion of calculation and the method of integration (Runge-Kutta with a fix or an adaptive step).
  • Other functions have been added: matrixunit, symmetryparameter, correlatedsignal, btw, avoidedcrossing, avoidedcrossings, minima, maxima.
  • Minor errors in the code has been fixed.
Version 0.9.9.0 (9th April 2009)
All platforms: Setup file (3.28MB) ZIP archive (3.83MB)
Forced 32-bit: Setup file (3.31MB) ZIP archive (3.83MB)

Warning: The program requires the dot '.' to be set as a decimal separator.

List of all functions of the program

Name Description Parameters
' Disable array evaluation of an expression Commands to be calculated
- Operator - m (Int32 | Double | Vector | Matrix | PointD | DateTime | LongNumber | LongFraction)
...
! Operator ! (boolean NOT) Boolean value (Boolean)
!= Operator != (inequality) Value (Int32 | Double | Vector | Matrix | PointD | PointVector | String)
...
# Array evaluation of an expression Commands to be calculated
% Modulo operator Integer number (Int32);
Integer number (Int32)
&& Operator && (boolean product) Boolean value (Boolean)
...
* Operator * c (Int32 | Double | Vector | Matrix | PointD | PointVector | LongNumber | LongFraction);
c (Int32 | Double | Vector | Matrix | PointD | PointVector | LongNumber | LongFraction)
** Operator **, items of vectors and matrices are multiplied among one another c (Int32 | Double | Vector | Matrix | PointD | LongNumber | LongFraction)
...
/ Operator / Dividend (Int32 | Double | Vector | Matrix | PointD | PointVector | LongNumber | LongFraction);
Divisor (Int32 | Double | Vector | Matrix | PointD | PointVector | LongNumber | LongFraction)
// Operator //, items of vectors and matrices are divided among one another Dividend (Int32 | Double | Vector | Matrix | PointD | LongNumber | LongFraction)
...
: Operator * Starting point of the interval (Int32);
Ending point of the interval (Int32);
[Step if the interval (Int32) = 1]
; Operator ; (separator) [Commands to be calculated]
...
? Help to the function Name of a function
?? Full help for the given function (including names and types of the parameters) Name of a function
@ Mutes the output of a function Name of a function
^ Operator ^ (power) Root (Int32 | Double | Vector | Matrix | String | LongNumber | LongFraction);
Exponent (Int32 | Double | Vector)
^^ Operator ^^, power is calculated among the items of vectors and matrices Root (Int32 | Double | Vector | Matrix | LongNumber | LongFraction);
Exponent (Int32 | Double | Vector | Matrix)
|| Operator || (boolean sum) Boolean value (Boolean)
...
~ Operator ~ (joins numbers together into vector, joins strings and lists) Value (Double | Vector | PointD | PointVector | List | String | TimeSpan)
...
+ Operator + addend (Int32 | Double | Vector | Matrix | PointD | String | LongNumber | LongFraction)
...
< Operator < Value (Int32 | Double)
...
<= Operator <= (lesser or equal) Value (Int32 | Double)
...
= Operator of assignment Variable name or indexed item;
Value to be assigned
...
== Operator == (equality) Value (Int32 | Double | Vector | Matrix | PointD | PointVector | String)
...
> Operator > Value (Int32 | Double)
...
>= Operator >= (greater or equal) Value (Int32 | Double)
...
abbreviate Abbreviates a fraction Fraction (LongFraction)
abs Absolute value Variable x (Int32 | Double | PointD | Vector | PointVector | Matrix)
add Adds an element to the end of the list Variable;
Item to be added to the end of the list
...
addbefore Adds an element to the beginning of the list Variable;
Item to be added to the end of the list
...
addglobal Adds an element to the end of the list in the global context Variable;
Item to be added to the end of the list
...
arctan Arcus tangens of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
array Z argumentů funkce vytvoří řadu (Array) prvky řady
arrayfiletocolumn Text file of an array reform is such way that the items will be in one column separated by an empty line Name of the file (String);
Name of the file (String)
arrayfiletocolumns Text file of an array reform is such way that the items will be in the columns Name of the file (String);
Name of the file (String)
arrayfiletocolumnsy Text file of an array reform is such way that the items will be in the columns Name of the file (String);
Name of the file (String);
[Number of items with independent x values (Int32) = 1]
autocorrelation Returns the autocorrelation function of a vector up to a given lag t Vector (Vector);
Time shift of the signals (Int32) = 0
avoidedcrossing Finds precise position of the avoided crossing of two levels (minimum of their distance) Phase transition object (PT3);
Index of the first level (Int32);
Index of the second level (Int32);
Minimal b for the calculation (Double);
Maximal b for the calculation (Double);
Maximum energy of the eigenstate and additional parameters (Int32);
[Precision of the calculation (Double) = 1E-14]
avoidedcrossings Finds points of all avoided crossings for PT3 Phase transition object (PT3);
Maximum energy of the eigenstate and additional parameters (Int32);
[Precision of the calculation (Int32) = 10]
bandwidth Size of the band of a band matrix Matrix (Matrix)
basisquantumnumber Transforms the index of the basis vector into its quantum numbers and vice versa Quantum system (IQuantumSystem);
Index of an eigenvalue (eigenvector) / quantum numbers (Vector | Int32)
basistoev Transforms given state vector represented in basis components to a vector expressed in components of eigenvectors Quantum system (IQuantumSystem);
Ket vector (PointVector | Vector)
basisvector Returns a basis vector Quantum system (IQuantumSystem);
Index of an eigenvalue (eigenvector) / quantum numbers (Vector | Int32)
bc Vrací binomické číslo int; int
benford Returns a histogram according to Benford's law Vector (Vector);
[First digit for the Benford's law (Int32) = 0];
[Number of digits taken into account in the Benford's law (Int32) = 1]
besselj Returns the value of the Bessel function J (Bessel function of the first kind) Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
besseljd Returns the derivative of the Bessel function J Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
bessely Returns the value of the Bessel function Y (Bessel function of the second kind) Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
besselyd Returns the value of the Bessel function Y (Bessel function of the second kind) Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
binmean Calculates mean of a PointVector in each of a defined bin pointvector (PointVector);
Number of bins or an interval (Vector | Int32)
bounds For given dynamical system and energy determines the bounds (higher limit) in which the solution can be found Dynamical system (IDynamicalSystem);
Energy of the system (Double)
boxspectrum Computes spectrum the infinite-well box potential E=sum_i (omega*ni^2) for integer frequencies omega Maximum energy of the eigenstate and additional parameters (Int32);
Frequency in the distinct directions (Int32) = 0
...
boxspectrum3d Computes spectrum the 3D infinite-well box potential E = (hbar^2 pi^2)/(2ML^2)[(nx^2+ny^2)e^2a + nz^2 e^-4a] (with a volume conservation condition) Maximum energy of the eigenstate and additional parameters (Double);
Deformation (Double)
...
brody Value of Brody distribution Variable x (Double | PointD | Vector | PointVector | Matrix);
Brody parameter (Double)
btw Finds points of all avoided crossings for PT3 Matrix (Matrix);
[Critical value (Int32) = 4];
[Step if the interval (Int32) = 1]
cdfe Reads all accessible pieces of information about an izotope from http://cdfe.sinp.msu.ru/cgi-bin/muh/radchartnucl.cgi Proton number (Int32);
Mass number (Int32)
cdfemaxbeta Find the maximum value of the deformation parameter Result of the function CDFE (List);
[Which values of beta is going to be taken (0...Qmom, 1...B(E2), 2...Theory) (Int32) = 0]
cdfemaxq Find the maximum and minimum value of the quadrupole deformation with its errors Result of the function CDFE (List)
cdp The classical double pendulum system [mu (Double) = 1];
[lambda parameter (ratio of lengths) (Double) = 1];
[gamma parameter (gravity parameter) (Double) = 1]
cep The classical extensible pendulum system [nu parameter (Double) = 0]
cgcm Creates a ClassicalGCM class (nonrotating case with simple kinetic term) [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1]
cgcmj Creates a ClassicalGCMJ class (case with nonzero angular momentum) [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1]
cibm Creates a ClassicalIBM class Eta parameter of IBM (Double);
Chi parameter of IBM (Double)
clear Erase variable from the context Name of the variable
...
clearall Delete all variables from the context
clearexcept Erase all variables except specified ones from the context [Name of the variable]
...
clearglobal Erase variable from the global context Name of the variable
...
cm Calculates correlation matrix Matrix (Matrix);
[True if the signal should be normalized (Boolean) = True];
[Time shift of the signals (Int32) = 0]
computespectrum Computes spectrum of a LHOQuantumGCM object Quantum system (IQuantumSystem);
Maximum energy of the eigenstate and additional parameters (Vector | Int32);
[True if the eigenvectors is to be calculated (Boolean) = False];
[Number of computed eigenvalues (and eigenvectors) (Int32) = 0];
[Computing method (jacobi | LAPACKband) (String) = "lapackband"]
context Creates a new context [Commands that will be run on the new context];
[Name of a variable that will be copied from actual context]
...
convexconcave For GCM system returns the negative energy for which the border changes from convex to concave shape GCM class (GCM);
[0...Change of island shape, 1...Change of outer shape (Boolean) = True];
[Precision of the determination of the energy (Double) = 0.001]
correlatedsignal Polynomial regression of data Frequencies of the signals (Vector);
Phase shifts in the first region (Matrix);
Time length of the first region (Int32);
[Time length of the second (transitional) region (Int32) = 0];
[Phase shifts in the third region (Matrix)];
[Time length of the third region (Int32) = 0];
[Time base constant (Int32) = 256]
cos Cosine of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
cosh Hyperbolic cosine of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
cot Cotangent of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
coth Hyperbolic cotangent of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
crop Removes values from a vector or pointvector that are larger or smaller than given bounds Vector (Vector | PointVector);
Minimum x bound (Double);
Maximum x bound (Double);
[Minimum y bound (Double) = -1.79769313486232E+308];
[Maximum y bound (Double) = 1.79769313486232E+308]
cumul Returns a vector of cumulations sum_{i=0}^{k} s_{k} Vector (Vector)
cumulbrody Value of cumulative Brody distribution Variable x (Double | PointD | Vector | PointVector | Matrix);
Brody parameter (Double)
cumulbrodyfit Returns the best Brody fit according to chi square test Pointvector with cumulative spacings (PointVector);
[precision (Double) = 0.001]
cumulhistogram Creates a cumulative histogram of a vector with a given binning Vector (Vector);
[Number of bins or an interval (Vector | Int32)]
cumulhistogramstep Creates an exact cumulative histogram as a step function Vector (Vector)
d2 Returns the second derivative Vector (Vector);
[Starting point of the interval (Double) = 0];
[Step if the interval (Double) = 1]
deflate Given array transforms into one dimensional array Array to be deflated (TArray)
delta Calculates statistics v_{i} - v_{0} - i Vector (Vector)
delta3 Calculates the number variance Vector (Vector);
Interval in the format (min, max, num) (Vector)
denominator Numerator of a fraction Fraction (LongFraction)
densitymatrix Returns a vector or a matrix with the probability density of the wave function(s) Quantum system (IQuantumSystem);
Index of an eigenvector or eigenvectors (Array) (Int32 | TArray);
Interval in the format (min, max, num) (Vector)
...
determinant Calculates a determinant of the matrix Matrix (Matrix)
dfa Detrended fluctuation analysis of a given time series Vector (Vector);
[True if you want to include all points (Boolean) = False]
double Converts given value to a double precision number Value (Double | String | TimeSpan | LongNumber | LongFraction)
dpxy Transforms angles of DoublePendulum system to (X, Y) coordinates of each body Double pendulum system (ClassicalDP);
Variable x (PointD | PointVector)
dropcolumns Z matice odstraní zadané sloupce Matrix; indexy sloupců
droprows Z matice odstraní zadané řádky Matrix; indexy řádků
eigenmatrix Returns a matrix of components of eigenvectors arranged in matrix by indexes LHOQuantumGCM object (LHOQuantumGCM);
Index of an eigenvalue (eigenvector) / quantum numbers (Int32)
eigensystem Eigensystem of a matrix calculated using LAPACK library (function dsyev); before calculation it makes symmetrization of a matrix Symmetrix matrix (in other hand the matrix will be symmetrized) (Matrix);
[True if the eigenvectors is to be calculated (Boolean) = False]
emd Detrended fluctuation analysis of a given time series pointvector (PointVector);
[Number of iterations after the condition |#max - #min| <= 1 is reached (Int32) = 10];
[A special parameter for the symmetry condition |U+L|/|U,L| leq delta (Double) = 0];
[True if the flat parts of the level density is going to be considered as a source of maxima / minima (Boolean) = False]
energy For given dynamical system and position in the phase space calculates the energy Energy of the system (IDynamicalSystem);
Position in the phase space (Vector)
energymin For given dynamical system returns the minimum possible energy GCM class (ClassicalGCM)
entropy Entropy of eigenvalues Vector (Vector)
envelopematrixg Generates an envelope matrix in Gaussian form (according to PRL 65, 529 (1990)) Size of the matrix (Int32);
Variance of the distribution (Double)
equipotential For GCM system and given energy calculates equipotential contour GCM class (IGeometricalMethod);
Energy of the system (Double);
[Number of points of the equipotential contour (Int32) = 0];
[Number of points dividing the 2pi interval (Int32) = 0]
eulergamma Value of the Euler-Mascheroni gamma constant
evaluate Evaluates a user function User function (UserFunction);
[Parameter of the function]
...
evalues Vrátí vypočítané vlastní hodnoty kvantového systému QuantumSystem
evectors Vrátí vypočítané vlastní vektory kvantového systému QuantumSystem
evnumdiff Pro LHOQuantumGCM třídu a zadaný vlastní vektor vytvoří matici H|n> - E|n> LHOQuantumGCM; číslo vlastní funkce (int); oblast výpočtu (Vector, prvky (minx, maxx, numx, ...))
evtobasis Transforms given state vector expanded in eigenvectors components to a vector expressed in components of the basis Quantum system (IQuantumSystem);
Ket vector (PointVector | Vector)
exclude From the first vector excludes values contained in the second vector Vector (Vector);
Values to be excluded (Vector | Int32);
[Precision of the calculation (Double) = 1E-06]
exit Sends the request to close the program
exp Exponential of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
export Saves a variable to a file Name of the file (String);
Expression (or variable);
[Type of the file ("binary" or "text") (String) = "binary"];
[Additional informations (Vector) = ]
exportmatrix Export a matrix in three columns format: (x, y, value) Name of the file (String);
Matrix (Matrix);
[Minimum x value (Double) = Není číslo];
[Maximum x value (Double) = Není číslo];
[Minimum y value (Double) = Není číslo];
[Maximum y value (Double) = Není číslo]
exportvector3d Export three vectors in three columns format: (v, x, y) Name of the file (String);
Vector (Vector);
Vector (Vector);
Vector (Vector)
extendedcgcm1 Creates an ExtendedClassicalGCM class with mass proportional to beta^2 [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Parameter extending mass coeficient (Double) = 1];
[Parameter extending mass coeficient (Double) = 1]
extendedcgcm2 Creates an ExtendedClassicalGCM class with kinetic term proportional to beta^2 [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Parameter extending mass coeficient (Double) = 1];
[Parameter extending mass coeficient (Double) = 1]
factorial Factorial of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
fftspectrum Gives the spectrum of a vector using Fast Fourier Transform (FFT) Sampled signal (Vector | ComplexVector);
[Sampling rate of the signal (Double) = 1]
fillmatrix Fills a matrix with points that correspond to a given PointVector Matrix (Matrix);
pointvector (PointVector);
Value (Double) = 0;
Bounds of the accessible region (Vector);
[How to deal with already filled values ("keep" | "overwrite" | "average") (String) = "keep"]
...
fnames Returns names of all registered functions which begin with specified string [Name of a function (String) = ""];
[Additional informations (Boolean) = False]
fnval Returns the duration of the calculation
for Cyklus for inicializační příkaz; podmínka opakování; příkaz při každém provedení [; příkaz po ukončení]
fraction Exact fraction Numerator (Int32 | LongNumber);
[Denominator (Int32 | LongNumber) = 1]
fullhelp Full help for the given function (including names and types of the parameters) Name of a function
fullhelphtml Full help for all functions (including names and types of the parameters) in the HTML format
fullsmooth Smooths a vector in such a manner that all components before computed position are used for averaging Vector (Vector | PointVector)
function Creates a user function using the given text Text with the function content (String);
[Variable (String) = ""];
[Given context (Context)]
functiontext Returns the text of the function User function (UserFunction)
gamma Gamma function Variable x (Double | PointD | Vector | PointVector | Matrix)
gaussiansmooth Data of input pointvector interprets as mean values and standard deviations of a set of Gaussian functions Variable x (Double | PointD | Vector | PointVector | Matrix);
Coefficients of Gaussians (PointVector | Vector);
[Weight (Vector)]
getcolumns Returns selected columns from a matrix Matrix (Matrix);
Indexes of columns (Int32 | TArray)
...
getcontext Returns actual context
getdiagonal Gets the diagonal of a square matrix Square matrix (Matrix)
getfilecontext Returns the context from a file Name of the file
getglobalcontext Returns global context
getglobalvar Gets out a variable from the global context Name of the variable
getindex Returns indices of items which are in given relation with given number Vector (Vector);
Value (Double) = 0;
[Comparison operator ("==" | "!=" | ">" | "<" | ">=" | "<="); (String) = "=="]
getrows Returns selected rows from a matrix Matrix (Matrix);
Indexes of rows (Int32 | TArray)
...
getvar Returns a variable from a given context Given context (Context);
Name of the variable
getx Z bodu nebo vektoru bodů vybere souřadnice X PointD | PointVector
gety From point or pointvector separates coordinates y Point-type object (PointD | PointVector)
goe Value of Wigner GOE distribution Variable x (Double | PointD | Vector | PointVector | Matrix)
gparamhelp Help to one graph parameter Parameter name
gparams List of all graph parameters
graph Create graph [Data for curves (TArray | Vector | PointVector)];
[Data for background (mesh graph) (TArray | Matrix)];
[Error bars for data (TArray | Vector)];
[Parameters for the whole graph (String | Context)];
[Parameters for groups of data (TArray | String | Context)];
[Parameters for curves (TArray | String | Context)]
gse Value of Wigner GSE distribution Variable x (Double | PointD | Vector | PointVector | Matrix)
gue Value of Wigner GUE distribution Variable x (Double | PointD | Vector | PointVector | Matrix)
hamiltonianaction Action of a Hamiltonian on a given ket Quantum system (IQuantumSystem);
Ket vector (PointVector | Vector);
[True if the square of the operator is to be applied (Boolean) = False]
hamiltonianmatrix Returns Hamiltonian matrix of the given quantum system Quantum system (IQuantumSystem);
Maximum energy of the eigenstate and additional parameters (Vector | Int32)
hamiltonianmatrixsize Dimensions of the Hamiltonian matrix Quantum system (IQuantumSystem);
Maximum energy of the eigenstate and additional parameters (Vector | Int32)
hamiltonianmatrixtrace Returns the trace of the Hamiltonian matrix of a quantum system Quantum system (IQuantumSystem);
Maximum energy of the eigenstate and additional parameters (Vector | Int32)
help Vrátí nápovědu k zadané funkci název funkce
hermite Value of the Hermite polynomial Variable x (Double);
Order of the polynomial (Int32)
hh Creates a HenonHeiles class
hilberttransform Hilbert Transform of a time series Sampled signal (Vector);
[Sampling rate of the signal (Double) = 1]
histogram Returns the histogram of a vector (on a given interval) Vector (Vector);
Number of bins or an interval (Vector | Int32);
[Type of histogram ("point" | "line" | "bar") (String) = "point"]
hospectrum3d Computes spectrum the 3D harmonic oscillator potential Maximum energy of the eigenstate and additional parameters (Double);
Deformation (Double)
...
chemicalpotential Returns the chemical potential of the Strutinsky method for a given mass number Strutinsky object (Strutinsky);
Mass number (Int32)
cho Creates a Coupled harmonic oscillator class Coupling constant (Double);
[Mass (Double) = 1];
[Rigidity (Double) = 1]
if Podmínka for podmínka; příkaz splnění; příkaz nesplnění
imf Calculates one Intrinsic Mode Function pointvector (PointVector);
[pointvector (Int32) = 10];
[A special parameter for the symmetry condition |U+L|/|U,L| leq delta (Double) = 0];
[True if the flat parts of the level density is going to be considered as a source of maxima / minima (Boolean) = False]
import Read a file to a variable Name of the file (String);
[Type of the file ("binary" | "text" | "matlab" | "digits" | "mathmat" | "wav") (String) = "binary"];
[How many lines to omit (Int32) = 0]
initialcondition For given dynamical system and energy generates initial condition of a trajectory and returns it as Vector Dynamical system (IDynamicalSystem);
Energy of the system (Double);
[Plane of the section (Vector)];
[First coordinate of the phase space which will be stored (Int32)];
[Second coordinate of the phase space which will be stored (Int32)];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[True if only one orientation of the crossing of the plane shall be considered (Boolean) = False]
initialconditionx For given dynamical system and energy generates missing coordinate / momentum in the initial condition Dynamical system (IDynamicalSystem);
Energy of the system (Double);
[Initial conditions (Vector)];
[True if only one orientation of the crossing of the plane shall be considered (Int32) = False]
instantaneousfrequency Instantaneous frequency between two vectors Variable x (Vector);
Real part of a number (Vector);
Immaginary part of a number (Vector)
int Converts given value to an integer number Value (Int32 | Double | String | TimeSpan)
integrate Calculates an integral under given curve Curve (PointVector)
intersection Finds all intersection points of two pointvectors pointvector (PointVector);
pointvector (PointVector)
intervala Creates points for interval (as an array) Starting point of the interval (Double);
Ending point of the interval (Double);
Number of points in the interval (Int32)
intervalpv Creates points for interval (in the form PointVector(0, interval points)) Starting point of the interval (Double);
Ending point of the interval (Double);
Number of points in the interval (Int32)
intervalv Creates points for interval Starting point of the interval (Double);
Ending point of the interval (Double);
Number of points in the interval (Int32)
isequal Returns true if the values are equal within given difference [Maximal error (Double) = 0];
Value (Double)
...
iseven True if the number is even Integer number (Int32)
isnull True if a given expression is null [Value]
isodd True if the number is odd Integer number (Int32)
isregularps Returns true if the Poincare section on the given energy is fully regular; otherwise returns false Dynamical system (IDynamicalSystem);
Energy of the system (Double);
Number of points in the X direction (Int32);
Number of points in the Y direction (Int32);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = ""];
[Precision of the calculation (Double) = 0];
[True if the section at x == 0 should be computed (Boolean) = False]
isregulartrajectory Distinguishes using SALI whether the trajectory is regular (1) or chaotic (0) Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = ""];
[Precision of the calculation (Double) = 0]
jacobi Eigensystem of a matrix calculated using Jacobi method; before calculation it makes symmetrization of a matrix Symmetrix matrix (in other hand the matrix will be symmetrized) (Matrix)
joinarray Joins 1D Arrays into one array Data to be joined (TArray)
...
laguerre Value of the Laguerre polynomial Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Int32);
[Associated order of the polynomial (Double) = 0]
lastevelements Returns last elements of components of eigenvectors; all quantum numbers are taken into account LHOQuantumGCM object (LHOQuantumGCM);
Index of an eigenvalue (eigenvector) / quantum numbers (Int32);
[Order of the elements from the back (Int32) = 0]
lastevelementssumabs Returns absolute value of the sum of last elements of components of eigenvectors LHOQuantumGCM object = PavelStransky.Systems.LHOQuantumGCM
legendre Value of the Laguerre polynomial Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Int32)
length Returns length(s) or number of elements of a given object as an array Object with several dimensions (Vector | TArray | Matrix | List | PointVector | String)
leveltonumber Transforms the string value of the level angular momentum 1/2- and parity into the numerical form -0.5 and vice versa Level labeling (string format 1/2- or numerical format -0.5) (String)
lhoqgcma5d Creates an object that calculates eigenenergies of QuantumGCM in 5D basis preparing the Hamiltonian matrix by using algebraic relations [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmare Creates an object that calculates eigenenergies of QuantumGCM in radial 2D basis even in angular coordinate preparing the Hamiltonian matrix by using algebraic relations [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmaro Creates an object that calculates eigenenergies of QuantumGCM in radial 2D basis odd in angular coordinate preparing the Hamiltonian matrix by using algebraic relations [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmi5d Creates an object that calculates eigenenergies of QuantumGCM in 5D basis preparing the Hamiltonian matrix by integrating the basis functions in x-representation [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmic Creates an object that calculates eigenenergies of QuantumGCM in 2D cartesian basis (direct product of two 1D harmonic oscillators) preparing the Hamiltonian matrix by integrating the basis functions in x-representation; states with all possible (also nonfysical) angular momentum are included [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmir Creates an object that calculates eigenenergies of QuantumGCM in radial 2D basis in angular coordinate preparing the Hamiltonian matrix byintegrating the basis functions in x-representation; both odd and even states are included [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmirf Creates an object that calculates eigenenergies of QuantumGCM in 2D radial basis preparing the Hamiltonian matrix by integrating the basis functions in x-representation; states with all possible (also nonfysical) angular momentum are included [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
lhoqgcmiro Creates an object that calculates eigenenergies of QuantumGCM in radial 2D basis odd in angular coordinate preparing the Hamiltonian matrix by integrating the basis functions in x-representation [A parameter of GCM (Double) = -1];
[B parameter of GCM (Double) = 1];
[C parameter of GCM (Double) = 1];
[K (mass) parameter of GCM (Double) = 1];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
linearregression Polynomial regression of data Input data for the regression (PointVector | Vector)
list Creates a list of all parameters [Item to be added to the end of the list]
...
log Logarithm of the value (with specified base) Variable x (Double | PointD | Vector | PointVector | Matrix);
[Base of the logarithm (Double)]
loglog From both x and y values of a pointvector calculates log_10 pointvector (PointVector);
[Scale parameter (Double) = 1]
long Converts given value to a long integer number (with arbitrary precision) Value (Int32 | String)
lyapunov Calculates SALI dependence on time for given trajectory Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Time of the evaluation (Double);
[Time step for the result (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = ""];
[Precision of the calculation (Double) = 0]
matrixcolumn Given vectors put onto columns of a matrix Data for a column (TArray | Vector | List)
...
matrixrow Given vectors put onto rows of a matrix Data for a row (TArray | Vector | List)
...
matrixunit Creates a unit matrix Size of the matrix (Int32)
matrixzatona Transforms the matrix with indices (Z, A) to (Z, N) Matrix (Matrix)
max Vrací prvek s nejvyšší číselnou hodnotou Value (Vector | Matrix)
maxabs Vrací prvek s nejvyšší číselnou hodnotou v absolutní hodnotě Value (Vector | Matrix)
maxabsindex Vrací index prvku s nejvyšší číselnou hodnotou v absolutní hodnotě Value (Vector | Matrix)
maxima Returns maxima of a given function Dynamical system (IMinMax);
[Precision of the calculation (Double) = 0]
maxindex Vrací index prvku s nejvyšší číselnou hodnotou Value (Vector | Matrix)
mcd Maximal common divisor of given numbers Value (Int32 | LongNumber);
Value (Int32 | LongNumber)
...
mean Calculates mean of a vector Vector (Vector)
merge Merges lists into one list [Lists to be merged (List)]
...
min Vrací prvek s nejnižší číselnou hodnotou Value (Vector | Matrix)
minabs Vrací prvek s nejnižší číselnou hodnotou v absolutní hodnotě Value (Vector | Matrix)
minabsindex Vrací index prvku s nejnižší číselnou hodnotou v absolutní hodnotě Value (Vector | Matrix)
minima Returns minima of a given function Dynamical system (IMinMax);
[Precision of the calculation (Double) = 0]
minindex Vrací index prvku s nejnižší číselnou hodnotou Value (Vector | Matrix)
new Creates new object of a given type Type of a variable
...
norm Norm of the vector Vector which norm is calculated (Vector);
[Power of items (Double) = 2]
normalizedensity Normalizes the level density of a given vector into the form (0, ..., length - 1) Energy levels of a system (Vector)
nudatreadknownisotopes Reads all known isotopes from http://www-nds.iaea.org
nudatreadnucleus Reads all accessible pieces of information about a nucleus from http://www-nds.iaea.org Labeling of a nucleus (String)
numbervariance Calculates the number variance Vector (Vector);
Interval in the format (min, max, num) (Vector)
numerator Denominator of a fraction Fraction (LongFraction)
occupationnumber Returns the occupation numbers of the Strutinsky method for a given mass number Strutinsky object (Strutinsky);
Mass number (Int32)
operatoraction Action of an operator on a given ket Double pendulum system (QuantumDP);
Ket vector (PointVector | Vector);
[Type of the operator (Int32) = 0]
operatorexpectdiagonal Expectation value of the diagonal elements Double pendulum system (QuantumDP);
Index of an eigenvalue (eigenvector) / quantum numbers (Vector | Int32);
[Type of the operator (Int32) = 0]
orbit Finds a periodic orbit using Poincare sections Dynamical system (IDynamicalSystem);
Initial conditions (Vector);
[Number of points of the final section (Int32) = 0];
[Minimum points of the circle (Int32) = 0];
[Precision of the calculation (Double) = 0]
parity Vrátí paritu stavů LHOQuantumGCMIR
pax Returns the probability amplitude of the wave function in the required point (only 1D systems) Variable x (Double | PointD | Vector | PointVector | Matrix);
Quantum system (IQuantumSystem);
Index of an eigenvalue (eigenvector) / quantum numbers (Int32)
pcn Number of principal components of eigenvector Vector = PavelStransky.Math.Vector
peresinvariant Returns the Peres invariant of a quantum system Quantum system (IQuantumSystem);
[Type of Peres operator (0...L2, 1...H', 2...Hosc) (Int32) = 0]
peresinvariantg Creates matrix with Poincaré section by the plane y = 0 for 2D system; contours are determined by time averaged Peres invariant Dynamical system (IDynamicalSystem);
Energy of the system (Double);
Time of the evaluation (Double);
Number of points in the X direction (Int32);
Number of points in the Y direction (Int32);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0]
peresinvariantt Calculates SALI dependence on time for given trajectory Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Time of the evaluation (Double);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0]
phase Phase between two numbers or vectors Real part of a number (Double | Vector);
Immaginary part of a number (Double | Vector)
pi Value of Pi number
plateau Returns the plateau condition of the Strutinsky method for a given mass number (must be zero) Strutinsky object (Strutinsky);
Mass number (Int32)
play Plays a given vector Channels of the sound to play (Vector | TArray | PointVector);
[Parameters of the sound (sampleRate = 44100; bitsPerSample = 16) (Vector) = ]
poincare Calculates a Poincaré section for given energy or trajectory given by its initial condition Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Number of points of the final section (Int32);
Plane of the section (Vector);
First coordinate of the phase space which will be stored (Int32);
Second coordinate of the phase space which will be stored (Int32);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[True if only one orientation of the crossing of the plane shall be considered (Boolean) = False]
point Creates a point from two given numbers Variable x (Double);
Variable y (Double)
pointvector Converts given data to a pointvector Values of the pointvector (Vector | List | TArray | PointD);
[Y values of the pointvector (Vector | PointD)];
[Other points (PointD)]
...
poisson Value of Poisson distribution Variable x (Double | PointD | Vector | PointVector | Matrix)
polynom Data of input vector interprets as coeficients of polynom and return its value Variable x (Double | PointD | Vector | PointVector | Matrix);
Coeficients of polynom (Vector)
polynomintegrate Data of input vector interprets as coeficients of polynom and return its integral Variable x (Double | PointD | Vector | PointVector | Matrix);
Coeficients of polynom (Vector)
potentialroots For GCM system solves the equation Potential == Given energy GCM class (GCM);
Energy of the system (Double);
[Gamma coordinate of the GCM (Double) = 0]
primes Returns given number of primes Count (Int32)
print Writes a text (or variable) to the writer [Expression (or variable) = ""]
printclear Vymaže všechny výstupy
printline Writes a text (or variable) to the writer and begins new line [Expression (or variable) = ""]
probabilityamplitude Returns the probability amplitude of the wave function in the required point Quantum system (IQuantumSystem);
Index of an eigenvalue (eigenvector) / quantum numbers (Int32);
Value (Double)
...
pstimes Calculates times of crossing of the plane of Poincaré section for given energy or trajectory given by its initial condition Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Number of points of the final section (Int32);
Plane of the section (Vector);
First coordinate of the phase space which will be stored (Int32);
Second coordinate of the phase space which will be stored (Int32);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[True if only one orientation of the crossing of the plane shall be considered (Boolean) = False]
pt1 Creates a class PT1 for studying quantum phase transitions Mixing parameter of the two minima (Double);
[Angular frequency of the LHO basis (Double) = 1];
[Planck constant (Double) = 0.01]
pt1potential Value of the potential of the system PT1 Variable x (Double | PointD | Vector | PointVector | Matrix);
Mixing parameter of the two minima (Double)
pt2 Creates a class PT2 for studying quantum phase transitions Mixing parameter of the two minima (Double);
[Angular frequency of the LHO basis (Double) = 1];
[Planck constant (Double) = 0.01]
pt2potential Value of the potential of the system PT2 Variable x (Double | PointD | Vector | PointVector | Matrix);
Mixing parameter of the two minima (Double)
pt3 Creates a class PT3 for studying quantum phase transitions (CASP potential) A parameter of GCM (Double);
B parameter of GCM (Double);
[Angular frequency of the LHO basis (Double) = 1];
[Planck constant (Double) = 0.01]
pt3potential Value of the potential of the system PT3 Variable x (Double | PointD | Vector | PointVector | Matrix);
A parameter of GCM (Double);
B parameter of GCM (Double)
ptsumln Returns sum of logarithms of differences between E_i and other energies Phase transition object (PT1);
[Index of an eigenvalue (eigenvector) / quantum numbers (Int32) = 0]
pv2dtomatrix Convert an array of pointvectors into a matrix Array or list of pointvectors (List | TArray);
Interval in the format (minx, maxx, numx) (Vector);
Interval in the format (miny, maxy, numy) (Vector);
Interval in the format (minz, maxz, numz) (Vector)
qdp The quantum double pendulum system [mu (Double) = 1];
[lambda parameter (ratio of lengths) (Double) = 1];
[gamma parameter (gravity parameter) (Double) = 1];
[Parameter of the ambiguity of the L_2^2 term in the kinetic term (usually 0...1) (Double) = 0]
qep The quantum extensible pendulum system [nu parameter (Double) = 0];
[Stiffness of the harmonic basis (Double) = 1];
[Planck constant (Double) = 0.01]
qspheroid Creates Quantum Spheroid class Deformation (Double) = 0
qsturmcoulomb Creates a quantum SturmCoulomb class Intensity of the magnetic field (Double) = 0
quantumtemperature Calculates a temperature using expression Tr(Ro H) = K Quantum system (IQuantumSystem);
Mean energy (Double)
randombrody Value with Brody distribution Brody parameter (Double)
randomg Generates Gaussian distributed random numbers with given variance and mean [Variance of the distribution (Double) = 1];
[Upper bound (Double) = 1]
randomgoe Value with Wigner GOE distribution
randomgse Value with Wigner GSE distribution
randomgue Value with Wigner GUE distribution
randommatrixsg Generates a symmetric matrix with Gaussian distributed components (according to PRL 65, 529 (1990)) Size of the matrix (Int32)
randompoisson Value with Poisson distribution
randomu Generates uniformly distributed random numbers between given limits [Lower bound (Double) = 0];
[Upper bound (Double) = 1]
randomvectorbrody Generates a vector with Brody distributed components Length of the vector (Int32);
Brody parameter (Double)
randomvectorg Generates a vector with Gaussian distributed components Length of the vector (Int32);
[Variance of the distribution (Double) = 1];
[Upper bound (Double) = 0]
randomvectorgoe Generates a vector with Wigner GOE distributed components Length of the vector (Int32)
randomvectorgse Generates a vector with Wigner GSE distributed components Length of the vector (Int32)
randomvectorgue Generates a vector with Wigner GUE distributed components Length of the vector (Int32)
randomvectorpoisson Generates a vector with Poisson distributed components Length of the vector (Int32)
randomvectoru Generates a vector with uniformly distributed components Length of the vector (Int32);
[Lower bound (Double) = 0];
[Upper bound (Double) = 1]
regression Polynomial regression of data Input data for the regression (PointVector);
Order of the polynomial (Int32)
regularitybreakcurvature Returns the energy for which there should be, according to the geometrical theory of chaos, the transition between regular and chaotic behaviour GCM class (ClassicalGCM);
Minimum considered energy (energy for which the system is fully regular) (Double);
Maximum considered energy (energy for which the system is chaotic) (Double);
[Number of points dividing the 2pi interval (Int32) = 0];
[Precision of the determination of the energy (Double) = 0.001]
regularitybreaksali Returns the energy for which the regular behavior starts breaking into the chaotic Dynamical system (IDynamicalSystem);
Minimum considered energy (energy for which the system is fully regular) (Double);
Maximum considered energy (energy for which the system is chaotic) (Double);
Number of points in the X direction (Int32);
Number of points in the Y direction (Int32);
[Precision of the determination of the energy (Double) = 0.001];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = ""];
[Precision of the calculation (Double) = 0];
[True if the section at x == 0 should be computed (Boolean) = False]
removebadpoints Removes bad points (NaN, Infinity) from Vector or PointVector Object that contains bad points (NaN, Infinity) (Vector | PointVector)
replacebadpoints Replaces bad points (NaN, Infinity) in Vector or PointVector by a given value Object that contains bad points (NaN, Infinity) (Vector | PointVector | Matrix);
[Value (Double) = 0]
replaceinterval Replaces values from specified interval with new value Variable x (Double | PointD | Vector | PointVector | Matrix);
Minimal value to be replaced (Double);
Maximal value to be replaced (Double);
New value (Double)
replacevalue Replaces a specified value with other one Variable x (Double | PointD | Vector | PointVector | Matrix);
Old value (Double);
New value (Double)
safevalue Gets the value of the variable from the context; If there the variable does not exist, returns default value. Variable;
Default value of the variable
sali Calculates SALI dependence on time for given trajectory Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Time of the evaluation (Double);
[Time step for the result (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = ""];
[Precision of the calculation (Double) = 0]
salig Creates matrix with Poincaré section by the plane y = 0 for 2D system; contours are determined by SALI Dynamical system (IDynamicalSystem);
Energy of the system (Double);
Number of points in the X direction (Int32);
Number of points in the Y direction (Int32);
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = ""];
[Precision of the calculation (Double) = 0];
[True if the section at x == 0 should be computed (Boolean) = False];
[True if only one orientation of the crossing of the plane shall be considered (Boolean) = False]
sample Samples the pointvector in the points of the given vector pointvector (PointVector);
Sapmpling points (Vector)
save Saves current document into a file [Name of the file (String) = ""]
savenow Saves current document into a file (in current thread) [Name of the file (String) = ""]
setcontext Sets a new context Given context (Context)
setdiagonal Given value or Vector of values put onto diagonal of square matrix Square matrix (Matrix);
Value(s) to be put onto diagonal (Vector | Double)
setglobalcontext Sets a new global context Given context (Context)
setglobalvar Sets a variable into the global context Name of the variable;
[Value]
setgraphparams Sets new parameters to a graph Graph object (created usually by graph command) (Graph);
[Parameters for the whole graph (String | Context)];
[Parameters for groups of data (TArray | String | Context)];
[Parameters for curves (TArray | String | Context)]
setnondiagonal Given value put onto nondiagonal elements of square matrix Square matrix (Matrix);
Value to be put instead of all nondiagonal elements (Double)
shellcorrection Returns the shell corrections of the Strutinsky method for a given mass number Strutinsky object (Strutinsky);
Mass number (Int32)
shotnoise Generates a vector with shot noise values Length of the vector (Int32);
a (Vector);
[Upper bound (Double) = 1];
[Poissonian intensity (Double) = 1]
show Shows a graph Graph object (created usually by graph command) (Graph | TArray);
[Name of the graph (will be shown in the graph caption) (String) = "Graph"];
[Number of columns in an array of graphs (Int32) = 1];
[Position of the window (PointD) = X = -1, Y = -1];
[Size of the window (PointD) = X = -1, Y = -1]
simplexvolume Calculates the volume of a simplex given by the vectors of the matrix Matrix (Matrix)
sin Sine of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
sinh Hyperbolic sine of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
smooth Smooths a vector Vector (Vector | PointVector)
smoothleveldensity Returns the smooth level density by the Strutinsky method Variable x (Double | PointD | Vector | PointVector | Matrix);
Strutinsky object (Strutinsky)
solve Solves an equation "the user function == zero" User function (UserFunction);
Minimum x value (Double);
Maximum x value (Double);
[Precision of the calculation (Double) = 0];
[Parameter of the function]
...
sort Ascending sort of the object (with keys according to the sorting will be done) Object to be sorted (ISortable);
[Keys for sorting (ISortable)]
sortdesc Descending sort of the object (with keys according to the sorting will be done) Object to be sorted (ISortable);
[Keys for sorting (ISortable)]
spacing Calculates neighbour spacing of vector components v_{i+j} - v_{i} Vector (Vector);
[Distance of the neigbour components (Int32) = 1]
sphericalbesselj Returns the value of the Spherical Bessel function j Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
sphericalbesseljd Returns the value of the derivative of the Spherical Bessel function j Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
sphericalbesseljzero Returns a given number of zeros of the spherical Bessel function j Order of the polynomial (Double);
Number of zeros (Int32);
[Precision of the calculation (Int32) = 1E-06]
sphericalbessely Returns the value of the Spherical Bessel function y (Spherical Neumann function) Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
sphericalbesselyd Returns the value of the Spherical Bessel function y (Spherical Neumann function) Variable x (Double | PointD | Vector | PointVector | Matrix);
Order of the polynomial (Double)
spline Creates a spline object pointvector (PointVector)
splinevalue Value of the Spline interpolation Variable x (Double | PointD | Vector | PointVector | Matrix);
Spline object (Spline)
sqrt Square root of the value Variable x (Double | PointD | Vector | PointVector | Matrix);
[Order of square root (Double | Int32) = 1]
stairsx Creates stairs from a pointvector pointvector (PointVector)
standardmapping Creates a time series of the standard mapping with given initial conditions Stochasticity parameter (Double);
Time of the evaluation (Int32);
Initial value of the variable r (Double);
Initial value of the variable theta (Double)
string Vrátí hodnoty jako řetězec int | double | Point | Vector | PointVector | Matrix | DateTime | string [; formát (string)]
strutinsky Returns an object dealing with Strutinsky corrections Energy of the system (Vector);
Order of the polynomial (Int32);
Range of the interaction (Double | Vector)
sum Sum of all elements in the object Object with several dimensions (Vector | Double | Int32 | Matrix)
sumabs Sum of absolute values of all elements in the object Object with several dimensions (Vector | Double | Int32 | Matrix)
sumsquare Sum of squares of values of all elements in the object Object with several dimensions (Vector | Double | Int32 | Matrix)
swapxy Swaps X and Y coordinates Object with x and y coordinates (PointD | PointVector)
symmetryparameter Symmetry parameter of eigenvector Vector = PavelStransky.Math.Vector
tan Tangent of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
tanh Hyperbolic tangent of the value Variable x (Double | PointD | Vector | PointVector | Matrix)
tdmeanoperator Thermodynamical mean value of a Peres operator Quantum system (IQuantumSystem);
Temperature (Double);
[Type of Peres operator (0...L2, 1...H', 2...Hosc) (Int32) = 0]
testarpack Generates randomly a symmetric sparse matrix and diagonalizes it Length of the vector (Int32);
Number of nonzero elements (Int32);
Number of computed eigenvalues (and eigenvectors) (Int32)
testarray Vytvoří testovací řadu ve formátu (000, 001, ...) dimenze1 (int)[; dimenze2 (int) ...]
testwww Tries to read text from specified URI [URI (link) (String) = "www.seznam.cz"]
threebody Creates ThreeBody class [Masses of the bodies (Vector) = ]
time Returns the duration of the calculation Commands to be calculated
timeevolution Time evolution of a given ket Quantum system (IQuantumSystem);
Ket vector (PointVector | Vector);
Time of the evaluation (Double) = False
timenow Returns the current time
toarray Given non-array object change to an array. Object to be converted to array (FileData | List | Vector)
trace Trace of a given matrix Matrix (Matrix)
traffic Creates a Traffic class [Number of points in the X direction (Int32) = 10];
[Number of points in the Y direction (Int32) = 10];
[Length of the street in the X direction (Int32 | Vector) = 15];
[Length of the street in the Y direction (Int32 | Vector) = 15];
[Topology of the traffic system (boundary conditions) ("cyclic" | "SingleMoebius" | "SimpleMoebius") (String) = "cyclic"]
trafficic Generates initial conditions for the traffic system Traffic class (Traffic);
Value for initial condition (Double | Vector);
[Type of the initial condition ("probability" | "total" | "street") (String) = "probability"]
trafficmatrix Returns a matrix showing the state of the traffic system Traffic class (Traffic)
trafficparams Sets the parameters of the traffic system Traffic class (Traffic);
[The distance of the sensor from the crossing (Int32) = -1];
[The short distance for the incomming cars (Int32) = -1];
[The short distance for the outgoing cars (outgoing street stopped) (Int32) = -1];
[Minimum green time of the traffic lights (Int32) = -1];
[Maximum tolerance for the incomming cars (Int32) = -1];
[Maximum number of cars in the short distance that will pass the lights (Int32) = -1]
trafficrun Runs the traffic system for several time steps Traffic class (Traffic);
[Time of the evaluation (Int32) = 1];
[Number of points from each side to cut the boundary (Int32) = 0]
trafficstep Makes a step of the traffic system Traffic class (Traffic);
[Time of the evaluation (Int32) = 1]
trajectorylength For given energy or a trajectory given by its initial condition calculates the length of the trajectory Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Time of the evaluation (Double);
[Time step for the result (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0]
trajectorym For given energy or a trajectory given by its initial condition calculates the trajectory; the result is returned by a matrix in the form (time, x, y, ..., px, py, ...) Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Time of the evaluation (Double);
[Time step for the result (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0]
trajectoryp For given energy or a trajectory given by its initial condition calculates the trajectory; the x, y coordinates of the result is returned by a PointVector Dynamical system (IDynamicalSystem);
Initial condition of a trajectory or energy if the trajectory is randomly chosen (Vector | Double);
Time of the evaluation (Double);
[Time step for the result (Double) = 0];
[Method of Runge-Kutta calculation (Normal | Adapted | Energy) (String) = "normal"];
[Precision of the calculation (Double) = 0]
transpose Transposition of a matrix Matrix (Matrix)
tsintegrate Integrates a time series S_{i}=sum_{j=1}^{i}(s_{j}-) Vector (Vector)
twobody Creates a ClassicalGCM class (nonrotating case with simple kinetic term) [Masses of the bodies (Vector) = ]
type Type of the value Value
unfolding Unfolds given data Energy levels of a system (Vector);
Parameter of the function (Int32);
[Type of the unfolding procedure ("cpolynom") (String) = "cpolynom"]
use Pokud je zadán název funkce, vrátí její použití, jinak vytvoří řadu (Array) s použitím všech zaregistrovaných funkcí [název funkce]
usecontext Uses the given context for specified calculations Given context (Context);
[Commands to be calculated];
[Variable]
...
variance Calculates variance of a vector Vector (Vector)
vector Convert given data to a vector [Items of vector (TArray | Double | Int32 | Matrix | List | Vector)]
...
vmatrix cal_{V} matrix (PRL 98, 234301 (2007), expression (27)) GCM class (IGeometricalMethod);
Energy of the system (Double);
Variable x (Double);
Variable y (Double)
vmatrixg Creates matrix with Poincaré section by the plane y = 0 for 2D system; contours are determined by SALI GCM class (IGeometricalMethod);
Energy of the system (Double);
Interval in the format (minx, maxx, numx) (Vector);
Interval in the format (miny, maxy, numy) (Vector);
[Index of the eigenvalue (0 is the highest one) (Int32) = 0]
vmatrixzero For GCM system and given energy calculates the line where the given eigenvalue of V matrix is zero GCM class (IGeometricalMethod);
Energy of the system (Double);
[Number of points of the equipotential contour (Int32) = 0];
[Number of points dividing the 2pi interval (Int32) = 0];
[Index of the eigenvalue (0 is the highest one) (Int32) = 0]
vrenorm
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